Off the top of my head –
What are his reasons for wanting mixed dancing? Not that any reason justifies it, but it can make it easier to approach the topic. Does he have family members who are insistent on mixed dancing? Does he lack the sensitivity to kedusha? Is he afraid of what his “friends” or the kalla’s side will say?
If it’s a matter of ta’ava and lack of kedusha, perhaps you can try to explain that one’s chasuna sets a foundation. It’s a fresh start, sets the tone for the future . . . Keeping the genders separate allows everyone there to focus on what a chasuna really is and focus on bringing simcha to the chosson and kalla. If the setting is skewed, it can affect the marriage.
Start off by finding something that he will for sure agree on. I imagine that any rational person recognizes that a chasuna is a special time, even if the person doesn’t understand just how special a time it is. Perhaps ask him what his goals are for marriage, to try to get him thinking in a more spiritual direction.
Yelling and arguments probably won’t help. Food for thought can.
And most of all, before and after you speak to him, and silently as you speak to him, beg HaShem to put the right words in your mouth and to open his heart to Torah truths. Remember that you are doing this, not because you want to be the hero who got your friend to not have mixed dancing at his chasuna, but because you want to do ratzon HaShem and help others do ratzon HaShem.
Hatzlocha.